Solve x^2y+2xy-7y=x^2+34x-71

$$x ^ { 2 } y + 2 x y - 7 y = x ^ { 2 } + 34 x - 71$$

Solve for y

$$y=-\frac{71-34x-x^{2}}{x^{2}+2x-7}$$

$$x\neq 2\sqrt{2}-1\text{ and }x\neq -2\sqrt{2}-1$$

Steps for Solving Linear Equation

Combine all terms containing y.

$$\left(x^{2}+2x-7\right)y=x^{2}+34x-71$$

Divide both sides by x^{2}+2x-7.

$$\frac{\left(x^{2}+2x-7\right)y}{x^{2}+2x-7}=\frac{x^{2}+34x-71}{x^{2}+2x-7}$$

Dividing by x^{2}+2x-7 undoes the multiplication by x^{2}+2x-7.

$$y=\frac{x^{2}+34x-71}{x^{2}+2x-7}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{2\sqrt{2\left(y-9\right)\left(y-5\right)}-y+17}{y-1}\text{; }x=\frac{-2\sqrt{2\left(y-9\right)\left(y-5\right)}-y+17}{y-1}\text{, }&y\neq 1\\x=2\text{, }&y=1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2\sqrt{2\left(y-9\right)\left(y-5\right)}-y+17}{y-1}\text{; }x=\frac{-2\sqrt{2\left(y-9\right)\left(y-5\right)}-y+17}{y-1}\text{, }&y\geq 9\text{ or }\left(y\neq 1\text{ and }y\leq 5\right)\\x=2\text{, }&y=1\end{matrix}\right.$$